find ( g(x) ), where ( g(x) ) is the reflection across the ( y )-axis of ( f(x)=|x| ).\nwrite your answer in…

find ( g(x) ), where ( g(x) ) is the reflection across the ( y )-axis of ( f(x)=|x| ).\nwrite your answer in the form ( a|x - h|+k ), where ( a ), ( h ), and ( k ) are integers.\n( g(x)= )

find ( g(x) ), where ( g(x) ) is the reflection across the ( y )-axis of ( f(x)=|x| ).\nwrite your answer in the form ( a|x - h|+k ), where ( a ), ( h ), and ( k ) are integers.\n( g(x)= )

Answer

Explanation:

Step1: Recall the reflection rule

When a function ( y = f(x) ) is reflected across the ( y )-axis, the transformation is ( y = f(-x) ). For ( f(x)=\vert x\vert ), substituting ( -x ) for ( x ), we get ( g(x)=\vert -x\vert ).

Step2: Simplify the expression

Since ( \vert -x\vert=\vert x\vert) (because the absolute value of a number and its negative are equal, i.e., for any real number ( a), ( \vert a\vert=\vert -a\vert)), and in the form ( a\vert x - h\vert + k), here ( a = 1), ( h=0), ( k = 0).

Answer:

(g(x)=1\vert x-0\vert + 0=\vert x\vert)